Question Number 84106 by jagoll last updated on 09/Mar/20
$$\int\:\frac{\mathrm{x}^{\mathrm{4}} }{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=\:? \\ $$
Commented by MJS last updated on 09/Mar/20
$${t}=\sqrt{\mathrm{sin}\:{x}}\:\rightarrow\:{dx}=\frac{\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}{\mathrm{2}{x}}{dt} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int\left(\mathrm{sin}\:{t}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} {dt} \\ $$$$\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{using}\:\Gamma\left({x}\right) \\ $$$$\mathrm{Sir}\:\mathrm{Tanmay}\:\mathrm{knows}\:\mathrm{how} \\ $$